QUIZ REVIEW What to study and example problems...

General Topics and Definitions Linear Pairs and Vertical Pairs of Angles. Use them to solve problems. Linear Pairs and Vertical Pairs of Angles. Use them to solve problems. Know all in class definitions—there are lots of them! Know all in class definitions—there are lots of them! Complimentary/Supplementary Complimentary/Supplementary Naming Polygons Naming Polygons Sum of angles in a polygon, diagonals in a polygon Sum of angles in a polygon, diagonals in a polygon Basic circle definitions and properties, arc measures Basic circle definitions and properties, arc measures

Example x FIND x. a b

Solution 1 First, solve for a, as 133 and angle a are LINEAR PAIRS. Their sum is a = 180.  a = 47. Next, find b. It has a vertical angle equal to 57 degrees. Since vertical angles are congruent, b = 57. Lastly, find x by applying the triangle angle sum theorem x = = x = x a b 57

Example 2 Name the shapes as specific as possible: Name the shapes as specific as possible: CH R I S P Q R S T I M X Y Z

Example 3 What is the measure of one angle in a regular octagon? What is the measure of one angle in a regular octagon? How many diagonals are there in an octagon? How many diagonals are there in an octagon?

Solution 3 To find the sum of the angles in ANY polygon, remember our formula: To find the sum of the angles in ANY polygon, remember our formula: (n-2)180 (where n = #sides) (n-2)180 (where n = #sides) (8-2)180 = 6(180) = (8-2)180 = 6(180) = There are 8 angles in a regular octagon, each of equal measure: 1080/8 = 135.

Solution 3 cnt’d How do we find diagonals?? How do we find diagonals?? n(n-3)/2 (where n = # sides) n(n-3)/2 (where n = # sides) There are 8 sides in an octagon, thus: There are 8 sides in an octagon, thus: 8(8-3) / 2 8(8-3) / 2 8(5) / 2 = 40/2 = 20 diagonals! 8(5) / 2 = 40/2 = 20 diagonals!

Example 4 48 A B C D Suppose A is the center of the cirlce. Name the radii. AB, AC, AD What is the diameter? BD AC = 6cm. BD = ? 12cm Arc BC = ? Arc DC = ? Arc BDC = ?

As for the arcs... The central angle ∠ BAC = 48° The central angle ∠ BAC = 48° The central angle measure is the same as the arc that it creates. Therefore, arc BC = 48°. The central angle measure is the same as the arc that it creates. Therefore, arc BC = 48°. Find ∠ DAC – it is a linear pair with ∠ BAC. Find ∠ DAC – it is a linear pair with ∠ BAC ∠ DAC = ∠ DAC =  ∠ DAC = 132° and  Arc DC = 132°. 48 A C D B The entire circle is 360°. Subtracting the 48° from 360° leaves you with the major arc BDC = 360 – 48 = 312°.

Review Assignment P.88, 89 #2-16 even P.88, 89 #2-16 even P.89, #17-20, #23-31 P.89, #17-20, #23-31 x x 52 a Find x and a. Find x.